{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:14:32Z","timestamp":1740165272747,"version":"3.37.3"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,5,30]],"date-time":"2022-05-30T00:00:00Z","timestamp":1653868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin\u22121xsinh\u22121x and tanh\u22121xtan\u22121x. The main results provide polynomial bounds using even quadratic functions and exponential bounds under the form eax2. Graph validation is also performed.<\/jats:p>","DOI":"10.3390\/axioms11060262","type":"journal-article","created":{"date-parts":[[2022,5,30]],"date-time":"2022-05-30T14:05:14Z","timestamp":1653919514000},"page":"262","source":"Crossref","is-referenced-by-count":2,"title":["Bounds for Quotients of Inverse Trigonometric and Inverse Hyperbolic Functions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5667-0431","authenticated-orcid":false,"given":"Sumedh B.","family":"Thool","sequence":"first","affiliation":[{"name":"Department of Mathematics Government Vidarbha, Institute of Science and Humanities, Amravati 444604, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8331-3920","authenticated-orcid":false,"given":"Yogesh J.","family":"Bagul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, K. K. M. College, Manwath Dist, Parbhani 431505, India"}]},{"given":"Ramkrishna M.","family":"Dhaigude","sequence":"additional","affiliation":[{"name":"Department of Mathematics Government Vidarbha, Institute of Science and Humanities, Amravati 444604, India"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Caen-Normandie, 14032 Caen, France"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,30]]},"reference":[{"key":"ref_1","first-page":"153","article-title":"Some new bounds for ratio functions of trigonometric and hyperbolic functions","volume":"61","author":"Chesneau","year":"2019","journal-title":"Indian J. 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